Irina Rezvyakova

Irina Rezvyakova
Russian Academy of Sciences | RAS · Steklov Mathematical Institute

PhD

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22
Publications
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30
Citations

Publications

Publications (22)
Article
In the late 1990s, Atle Selberg invented a new method, which had allowed him to prove that if a linear combination of Dirichlet L-functions satisfies a functional equation, then a positive proportion of its zeros lie on the critical line. The paper considers this method in detail for the general case of a linear combination of L-functions from the...
Research
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This is a manuscript, where we consider in details the method of A.~Selberg which allows one to prove under certain natural conditions that a positive proportion of non-trivial zeros of a linear combination of L-functions lie on the critical line. We provide all the necessary ingredients to prove this result in the case of a linear combination of d...
Article
Full-text available
In January, 2014, the I’st one-dayinternational “Conference to the Memory of A.A. Karatsuba on Number Theory and Applications” took place in Steklov Mathematical Institute of Russian Academy of sciences. The aims of this conferencewere presentationof newandimportantresultsin differentbranches of number theory (especially in branches connected with w...
Article
We prove for L-function attached to an automorphic cusp form for the Hecke congruence group $\Gamma_0(D)$, which is also an eigenfunction of all the Hecke operators, that a positive proportion of its non-trivial zeros lie on the critical line. This result extends the work of J.L. Hafner of 1983 where the case of the full modular group is considered...
Article
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We obtain a new lower bound for the number of zeros on intervals of the critical line for linear combinations of Hecke -functions.
Article
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We consider an automorphic cusp form of integer weight k ≥ 1, which is the eigenfunction of all Hecke operators. It is proved that, for the L-series whose coefficients correspond to the Fourier coefficients of such an automorphic form, the positive fraction of nontrivial zeros lie on the critical line. Key wordsautomorphic cusp form-Riemann zeta f...
Article
In this paper two theorems were obtained. In the first theorem it is proved that a positive proportion of non-trivial zeros lie on the critical line for L-functions attached to automorphic cusp forms for congruence-subgroups. Therefore, the class of functions satisfying a variant of Selberg’s theorem was extended. In the second theorem a new lower...
Article
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In this paper we consider certain 1-parametric family of Dirichlet series. For a particular value of the parameter the series turns into the Dirichlet series for the Riemann zeta function. We prove that almost every series of the family has analytic continuation to the half plane Re s > 1/2 where it doesn't vanish. The result was obtained before by...
Article
We get a lower bound for the number of simple zeros of the function on the critical line, where .
Article
We show that the proportion of the zeros of the th derivative of the Riemann -function (where is an integer) that are on the critical line is greater than .

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